Title :
The Estimation of the Fourth-Order Cumulant for Dependent Data: Consistency and Asymptotic Normality
Author_Institution :
Dept. of Electr. & Comput. Eng., Univ. of California, San Diego, CA, USA
fDate :
4/1/2010 12:00:00 AM
Abstract :
Let {Xi} be a stationary dependent random process with finite eight-order moments. For broad classes of processes (??-mixing and strongly mixing), we obtain the convergence in probability, with sharp rates, of the estimate of the fourth-order cumulant from n observations {Xi}i=1 n . We also establish the asymptotic distribution of the estimation error. The asymptotic expression of the variance is explicitly specified.
Keywords :
blind source separation; convergence of numerical methods; error statistics; higher order statistics; probability; asymptotic distribution; asymptotic normality; blind source separation; dependent data consistency; estimation error; finite eight-order moments; fourth-order cumulant estimation; probability convergence; stationary dependent random process; $rho$-mixing and strongly mixing processes; Asymptotic normality; convergence in probability; fourth-order cumulant;
Journal_Title :
Signal Processing, IEEE Transactions on
DOI :
10.1109/TSP.2009.2039729
